the question how do atoms, and proteins get to call themselves “I”s
is similar to the Godel thing where bunch of symbols in mathematics refer to themselves (in a theorem or something)
Tools for thinking
- isomorphism
- recursion
- paradox
- infinity
- formal systems
isomorphism:
- two complex structure can be mapped as parts into corresponding where such parts play similar role
- dont worry about the algebra definition
recursion:
- everything everywhere fibonacci and shit
- fractals
paradoxes:
- veridical, falsidical, antinomy
- Liar paradox: this sentence is not true
- Russel’s paradox: barber shaves only people who dont shave themselves
infinities:
- multiple types
formal system:
- thats where we start
Formal Systems
bag of 3 letters {M, I, U}
pull 2 lettes MI
4 rules:
- can attach U to the I: XI → XIU
- can extend next char if pre is M: MX → MXX
- can replace 3 I’s with U: MIII → MU
- Double pair of U’s drop away: UU → (poof)
Starting with MI - can you get MU?
when you are solving this puzzle - do you think above the system (as meta thinking)
- in life there are social systems and some people tell you to exit
- communism, schools, matrix
The p q hyphen system
- isomorphism to a single plus system
- happy happy horse apple
goal is to derive isomorphic system to universe (is reality a formal system?)
- elementary particles as symbols
- physics as inference rules
- question is - what kind of configurations are possible?
- is universe determnistic?
Recursions
- factorials and shit
- something about fancy nouns as recursive? english is also that?
- draws Tree using recursion and says it looks same in every graph - go zoom
- Koch curves
- if you add noise they kind of start to look like real structure
- Sierpinski noise
- iterative function system
- Mandelbrot set: z = z^2 + C
Godel Incompleteness Theorem
consistency: if P is true then in the same formal system not P should never be True incompleteness: all True statements are provable. If you cannot prove something how do you even now that it’s true? geometry: Euclidean vs non
which statements are True:
- The sky is Blue
- 1 + 1 = 2 (but modulo arithmetic or 1 raindrop + 1 raindrop)
Hilbert said maths is the thing man
- Any system as powerful as numbery theory which can prove its own consistency is inconsistent
- And also incomplete
This statement is not provable
- False → actually provable
- True → whatever its saying is a fact (unprovable)
Euclid postulates:
- 4 others
- There is a line and a point not on the line, you can draw a line that goes through that point and never intersects the other line
Here comes the hyperbolic geometry (which are consistent system)
Something about natural progression/series but how does it fits here?
Back to things:
- If recursion is fundamental and intelligent, why are humans bad at it?
- Kasparov intuits
Meaning of language (out of nowhere)
Meaning is not inherent, rather a relationship
- Apple has complex isomorphism in brain signals
Just ask Gemini lol